Question

The value of RootIndex 3 StartRoot x Superscript 10 Baseline EndRoot , when x = negative 2, can be written in simplest form as a RootIndex 3 Start Root b EndRoot, where
  a =
and b =
.

Answer 1

Answer:

The value of a = 8.

The value of b = 2.

Step-by-step explanation:

Given: $\sqrt[3]{x^{10}}$ where, x = -2

$x^{-10} = (-2)^{-10}$

Since, the power is even (10), the resultant will be a positive number.

So, we have:

$\sqrt[3]{(-2)^{-10}} = \sqrt[3]{2^{10}}$

Note that: $\sqrt[a]{x} = x^{\frac{1}{a}}$

Also, $x^a . x^b = x^{a + b}$

Therefore, we get:

$\sqrt[3]{2^{10}} = 2^{\frac{10}{3}}$

$= 2^{\frac{9 + 1}{3}}$

$= 2^{\frac{9}{3}} . 2^{\frac{1}{3}}$

$= 2^3 . \sqrt[3]{2}$

Hence, a = 8; b = 2

Hence, the answer.

Answer 2

Answer:

A= -8

B= -2

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